Using the methods of potential theory for solving direct geophysical problems for three-dimensional complex condition
New analytical solution of direct problem of gravity for a standard element with density changing with the depth by linear law has been obtained. Mathematical statement has been carried out and general solution of the problem has been given for valuation of strains and instantaneous velocities of mo...
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| Datum: | 2013 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch |
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S. Subbotin Institute of Geophysics of the NAS of Ukraine
2013
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| Online Zugang: | https://journals.uran.ua/geofizicheskiy/article/view/111343 |
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| Назва журналу: | Geofizicheskiy Zhurnal |
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Geofizicheskiy Zhurnal| _version_ | 1856543173067669504 |
|---|---|
| author | Pyatakov, Yu. V. Isaev, V.I. |
| author_facet | Pyatakov, Yu. V. Isaev, V.I. |
| author_sort | Pyatakov, Yu. V. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2020-10-07T10:46:54Z |
| description | New analytical solution of direct problem of gravity for a standard element with density changing with the depth by linear law has been obtained. Mathematical statement has been carried out and general solution of the problem has been given for valuation of strains and instantaneous velocities of movement of heterogeneous viscous medium under the impact of the Earth's gravity field. The solution has been determined with application of hydrodynamic potentials (threedimensional, ordinary and double layer). Mathematical statement has been considered and general solution of instable and stationary systems of thermal conductivity equation has been obtained for heterogeneous medium. It has been demonstrated that for numerical calculation of hydrodynamic and thermal potentials it is optimal to use the theory and standard technique for solving direct problems of gravity potential. Stability, accuracy and operation speed of the algorithms elaborated is demonstrated by calculations of test examples. |
| first_indexed | 2025-07-17T11:05:53Z |
| format | Article |
| id | journalsuranua-geofizicheskiy-article-111343 |
| institution | Geofizicheskiy Zhurnal |
| language | Russian |
| last_indexed | 2025-07-17T11:05:53Z |
| publishDate | 2013 |
| publisher | S. Subbotin Institute of Geophysics of the NAS of Ukraine |
| record_format | ojs |
| spelling | journalsuranua-geofizicheskiy-article-1113432020-10-07T10:46:54Z Using the methods of potential theory for solving direct geophysical problems for three-dimensional complex condition Pyatakov, Yu. V. Isaev, V.I. New analytical solution of direct problem of gravity for a standard element with density changing with the depth by linear law has been obtained. Mathematical statement has been carried out and general solution of the problem has been given for valuation of strains and instantaneous velocities of movement of heterogeneous viscous medium under the impact of the Earth's gravity field. The solution has been determined with application of hydrodynamic potentials (threedimensional, ordinary and double layer). Mathematical statement has been considered and general solution of instable and stationary systems of thermal conductivity equation has been obtained for heterogeneous medium. It has been demonstrated that for numerical calculation of hydrodynamic and thermal potentials it is optimal to use the theory and standard technique for solving direct problems of gravity potential. Stability, accuracy and operation speed of the algorithms elaborated is demonstrated by calculations of test examples. S. Subbotin Institute of Geophysics of the NAS of Ukraine 2013-03-01 Article Article application/pdf https://journals.uran.ua/geofizicheskiy/article/view/111343 10.24028/gzh.0203-3100.v35i2.2013.111343 Geofizicheskiy Zhurnal; Vol. 35 No. 2 (2013); 78-97 Геофизический журнал; Том 35 № 2 (2013); 78-97 Геофізичний журнал; Том 35 № 2 (2013); 78-97 2524-1052 0203-3100 ru https://journals.uran.ua/geofizicheskiy/article/view/111343/106344 Copyright (c) 2020 Geofizicheskiy Zhurnal https://creativecommons.org/licenses/by/4.0 |
| spellingShingle | Pyatakov, Yu. V. Isaev, V.I. Using the methods of potential theory for solving direct geophysical problems for three-dimensional complex condition |
| title | Using the methods of potential theory for solving direct geophysical problems for three-dimensional complex condition |
| title_full | Using the methods of potential theory for solving direct geophysical problems for three-dimensional complex condition |
| title_fullStr | Using the methods of potential theory for solving direct geophysical problems for three-dimensional complex condition |
| title_full_unstemmed | Using the methods of potential theory for solving direct geophysical problems for three-dimensional complex condition |
| title_short | Using the methods of potential theory for solving direct geophysical problems for three-dimensional complex condition |
| title_sort | using the methods of potential theory for solving direct geophysical problems for three-dimensional complex condition |
| url | https://journals.uran.ua/geofizicheskiy/article/view/111343 |
| work_keys_str_mv | AT pyatakovyuv usingthemethodsofpotentialtheoryforsolvingdirectgeophysicalproblemsforthreedimensionalcomplexcondition AT isaevvi usingthemethodsofpotentialtheoryforsolvingdirectgeophysicalproblemsforthreedimensionalcomplexcondition |